Congruences between modular forms have played a central role in modern number theory.  Mazur studied Eisenstein congruences to understand rational torsion on elliptic curves.  Ribet studied level raising and lowering congruences, and his work was further built up by Diamond and Taylor.  Congruences at ``Taylor—Wiles primes” play a key role in Wiles and Taylor—Wiles’ proof of Fermat’s Last Theorem.  In this talk we will present a framework for uniting many of these examples of congruences between modular forms.  The method leverages the modular representation theory of $\mathrm{PGL}_2(\mathbb{F}_p)$ at primes away from $p$.  Not only does the method produce congruences in a unified and predictable way, it also elucidates extra structure on the relevant Hecke algebra.  This is ongoing joint work with Robert Pollack and Preston Wake.